CN103411624B - The magnetic field sources scaling method and system of electromagnetic tracking system based on micromotion platform - Google Patents
The magnetic field sources scaling method and system of electromagnetic tracking system based on micromotion platform Download PDFInfo
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Abstract
The invention belongs to technical field of electromagnetic measurement, the magnetic field sources origin and initial attitude scaling method and system of specially a kind of electromagnetic tracking system based on three axle micromotion platforms.The calibration system of the present invention, by three axle micromotion platforms, magnetic sensor, two it is rotatable and realize that the magnetic field sources arbitrarily pointed in space and control process display device form, the demarcation of relative position and posture between magnetic field sources can be achieved.Specific scaling method is to be moved to 5 selected known coordinate points by three axle micromotion platforms control Magnetic Sensor；Recycle electromagnetic tracking system to position the locus of 5 points, obtain the spatial positional information between magnetic field sources and these points, then calculate initial relative position and posture between magnetic field sources.The magnetic tracking algorithm based on rotating excitation field is corrected according to calibration result, is remarkably improved positioning precision.
Description
Technical field
The invention belongs to technical field of electromagnetic measurement, and in particular to magnetic field sources relative position and initial in electromagnetic tracking system
The scaling method and system of posture.
Background technology
Electromagnetism tracks（Electromagnetic Tracking）, or electromagnetic field positioning, it is that one kind utilizes magnetic field or electricity
The locus of object and posture are detected in magnetic field and the method for real-time tracking.This method can be applied to leading for Minimally Invasive Surgery
Boat, also can operate with the fields such as virtual reality, 3-D supersonic imaging.System is tracked in the electromagnetism containing 2 or more than 2 magnetic field sources
In system, positioning/track algorithm will generally use the spatial relation between magnetic field sources, and the whether accurate direct shadow of position relationship
Ring tracking accuracy, it is therefore desirable to which the locus of electromagnetic tracking system magnetic field sources is demarcated.
Currently used scaling method is optical calibrating.Because the precision of optical positioning system is high, can obtain higher
Stated accuracy.But, cannot when there is barrier between light source and spotting, or when spotting is hidden in flight data recorder
Demarcated using optical positioning system.It is using optical positioning system it is difficult to orthogonal to three for electromagnetic tracking system
The origin of coil is demarcated.Therefore the practical application of optical positioning system demarcation has certain limitation.
The content of the invention
It is an object of the invention to propose a kind of magnetic field sources relative space position based on three axle micromotion platforms and initial appearance
The scaling method and system of state, the demarcation for the electromagnetic tracking system containing more than one magnetic field sources.
Calibration system proposed by the present invention is made up of following four parts：Magnetic field sources, magnetic sensor device, at control
Manage display device and three axle micromotion platforms；Wherein：
The magnetic field sources are 2, are formed by orthogonal three axial coil and corresponding three control drive circuits；Orthogonal three axle
Three electromagnet coil geometric centers of coil overlap；The origin of magnetic field sources 2 in the X-axis of magnetic field sources 1, two magnetic field sources origins it
Between distance be d, the Y-axis and Z axis of two magnetic field sources are parallel to each other；The electromagnet for forming magnetic field sources uses constant current exciting mode, by
Control process display device controls every group of exciting current intensity；Orthogonal three axial coil is simulating the bar magnet that space is arbitrarily pointed to；
The magnet sensor arrangement is fixed on three axle micromotion platforms, controls it accurately to be moved in space by three axle micromotion platforms
It is dynamic, measure the magnetic induction intensity of three orthogonal directions；The triaxial magnetic field sensor device includes：Three axis component sensors, one
Individual signal condition and analog to digital（AD）Modular converter, three axis component sensors are respectively intended to detect three orthogonal direction X ', Y '
And Z ' magnetic induction intensity, it is exported through follow-up signal condition and analog to digital（AD）Modular converter is sent into control process and shown
Showing device, handled by the sampling processing module samples in control process display device；
The control process display device is by control unit, algorithm unit, display output unit and three axle micromotion platform controls
Unit composition processed, wherein：
Described control unit includes three parts：Sampling processing module, exciting current intensity control module and micromotion platform
Control module；The sampling processing module is the I/O mouths that microprocessor carries, and signal condition and mould are come from for sampling processing
The signal of plan-data-converting block；The exciting current intensity control module is microprocessor according to the simulation bar magnet calculated
The exciting current of three quadrature coils of magnetic field sources corresponding to the anglec of rotation, the control for controlling magnetic field sources by I/O mouths drive electricity
Road, there is provided the excitation control to three axle quadrature coils, synthesize the required simulation bar magnet pointed to；The micromotion platform control module is
Microprocessor controls the movement of three axles of micromotion platform by I/O mouth output signals as requested, and thus drive be fixed on it is micro-
Magnetic Sensor on moving platform is moved to selected coordinate points（Such as n1, n2, n3 hereafter（Overlapped with m1）, m2, m3 five
Point）On；
The algorithm unit according to simulation magnetic bar rotation searching and can eventually point to sensor process in microprocessor internal
The rotation angle information of middle acquisition, with origin calibration algorithm, calculating magnetic field source 1, the origin of magnetic field sources 2；With initial
Posture calibration algorithm, calculating magnetic field source 1, magnetic field sources 2 each reference axis initial sensing；
The display output unit is the liquid crystal display and I/O mouths that are connected with microprocessor, for will be by algorithm unit
The calibration result being calculated is exported and shown over the display；
The three axles micromotion platform control unit is in microprocessor internal, the instruction pair exported as requested by I/O mouths
Three the mobile of axle of micromotion platform are accurately controlled；
The three axles micromotion platform by three mutually orthogonal tracks and can accurate movement in orbit fixing device group
Into for controlling magnetic sensor in space accurate movement.
In the present invention, the sensor can select magnetoresistive transducer, hall effect sensor or fluxgate sensor etc.,
Magnetic induction intensity for three orthogonal directions of measurement space.
In order to preferably describe the present invention, seven coordinate systems as shown in table 1 are defined according to right-hand rule, wherein
CS1 is global coordinate system, and CS6 is micromotion platform coordinate system, and reference coordinate system during calibration.
The coordinate system of table 1 defines
| Coordinate system title | Abbreviation | Description |
| Coordinate system 1 | CS1 | The original coordinate system of magnetic field sources 1 |
| Coordinate system 2 | CS2 | The preferable original coordinate system of magnetic field sources 2 |
| Coordinate system 3 | CS3 | When the x-axis of magnetic field sources 1（Bar magnet axis direction）During orientation sensor, the actual coordinates of magnetic field sources 1 |
| Coordinate system 4 | CS4 | When the x-axis of magnetic field sources 2（Bar magnet axis direction）During orientation sensor, the actual coordinates of magnetic field sources 2 |
| Coordinate system 5 | CS5 | Magnetic sensor coordinate system |
| Coordinate system 6 | CS6 | Micromotion platform coordinate system |
| Coordinate system 7 | CS7 | The actual original coordinate system of magnetic field sources 2 |
It is proposed by the present invention using the above-mentioned magnetic field sources relative space position based on three axle micromotion platforms and initial attitude
The scaling method of calibration system, is comprised the following steps that：
Step 1: calibration system is initialized；
Step 2: space known coordinate point is shifted to by three axle micromotion platforms control magnetic sensor device；
Step 3: the simulation bar magnet corresponding to magnetic field sources 1 and magnetic field sources 2, searches for and points to the magnetic sensor
Device；
Step 4: the bar magnet that recording magnetic field source 1, magnetic field sources 2 are simulated fills from initial position to magnetic sensor is pointed to
The horizontal and vertical anglec of rotation during putting；
Step 5: judge three axle micromotion platforms whether by magnetic sensor device move to five, space it is selected known to
Coordinate points, if NO, then repeat step three, four；If YES, then six are gone to step；
Step 6: under conditions of step 5 is positive result, with magnetic field sources origin calibration algorithm, calculating magnetic field
Source 1, the origin of magnetic field sources 2；
Step 7: with magnetic field sources initial attitude calibration algorithm, calculating magnetic field source 1, magnetic field sources 2 each reference axis it is initial
Point to.
The first step of the inventive method, it is after powering, micromotion platform, magnetic field sources 1 to be controlled by control process display device
Respective initial position is moved/turns to magnetic field sources 2；Three axles of specially micromotion platform are moved to the origin of coordinates, magnetic
Field source 1 and magnetic field sources 2 turn to both X-axis and are parallel to each other, and Y-axis is parallel to each other, and Z axis is parallel to each other（This is ideal situation, real
Border may have error, and this is also the purpose of posture demarcation of the present invention）.
The second step of the inventive method, it is that space known coordinate point is shifted to by micromotion platform control sensor.The numerical control
Three axle micromotion platforms include mutually orthogonal x, tri- tracks of y, z, and positioning precision reaches 0.1mm.Using the micromotion platform, magnetic is passed
Sensor is individually positioned in n1, n2, n3（Overlapped with m1）, on five points of m2, m3, and by subsequent step, by magnetic field sources 1, magnetic field
Source 2 positions to this five points.In CS6 coordinate systems, the requirement to this five points is as follows：
N3 and m1 is overlapped；
Point-blank, and the distance between n1, n2 are equal with the distance between n2, n3 by n1, n2, n3；
M1, m2, m3 are on another straight line not parallel with n1, n2, n3, and the distance between m1, m2 and m2, m3
The distance between it is equal.
3rd step of the inventive method, it is when sensor reaches n1, n2, n3（Overlapped with m1）, certain point in m2, m3
When, it is positioned by magnetic field sources 1, magnetic field sources 2.Specific practice is alternately swashed with constant current respectively by control process display device
The mode encouraged encourages orthogonal three axial coil of composition magnetic field sources；Described orthogonal three axial coil need to meet in the geometry of three coils
The heart overlaps, and the mutually orthogonal condition of axis of three coils；Described constant current drive alternative excitation mode, it is by each excitation
Cycle was divided into at least two periods, and in first period in constant current drive cycle, on x-axis transmitting coil giving amplitude is
Asin(φ)The exciting current of ampere, amplitude A is given on y-axis transmitting coilcos(φ)The exciting current of ampere is big to synthesize
Small is A amperes, is rotated in x-y planeφThe bar magnet of degree, controlφChange in 0-2 π, when simulation bar magnet orientation sensor is in x-y
During plane projection direction, sensor can detect maximum magnetic induction, and the anglec of rotation for now simulating bar magnet isφ ij （Whereini =1-2,Corresponding magnetic field sources 1 and magnetic field sources 2；j=1-5Five corresponding n1, n2, n3 (or m1), m2, m3 coordinate known points）；Afterwards, x
It is A that amplitude is given on axle transmitting coilsin(φ ij )* sin(θ)The exciting current of ampere, amplitude is given on y-axis transmitting coil
For Acos(φ ij ) * sin(θ)The exciting current of ampere, it is A that amplitude is now given on z-axis transmitting coilcos (θ)Ampere
Exciting current, you can synthesis in the simulation bar magnet rotated perpendicular to x-y plane；ControlθChange in the range of 0- π, work as simulation
During bar magnet orientation sensor, sensor can detect maximum magnetic induction, now simulate the anglec of rotation of the bar magnet in vertical plane
Spend and beθ ij .The anglec of rotation of record nowθ ij 。
4th step of the inventive method is bar magnet that recording magnetic field source 1,2 is simulated from initial position to orientation sensor
During feathering angleφ ij （Bar magnet is simulated to be rotated to orientation sensor in plane throwing by initial position in x-y plane
Anglec of rotation during shadow）With vertical rotary angleθ ij （That is simulation bar magnet is rotated to finger in the plane perpendicular to x-y by initial position
To anglec of rotation during sensor）.
5th step of the inventive method, complete magnetic field sources and be pointed to n1, n2, n3（Overlapped with m1）, five points of m2, m3 biography
Sensor positions respectively.
6th step of the inventive method, it is to use magnetic field sources origin calibration algorithm, the origin in calculating magnetic field source 1,2 is sat
Mark（xi,yi,zi）；Therefore, Magnetic Sensor can be placed on three points of known spatial coordinate, you can establish reflection simulation magnetic
The equation group of three equations composition of geometrical relationship between rod and Magnetic Sensor, and then solve bar magnet pivot coordinate.But three
Equation equation group not necessarily has solution, and the present invention devises the scheme for establishing 5 equation groups, is not increasing method complexity excessively
In the case of, improve the stability of algorithm.The scaling scheme of different number magnetic field sources can be analogized to obtain by the present invention.
Referring to the drawings 4（Magnetic field sources 1 are only depicted, magnetic field sources 2 can be drawn with same procedure）By equation group（1）It can calculate
Go out coordinate of the origin of magnetic field sources 1,2 in CS6（x1,y1,z1）、（x2,y2,z2）：
（1）
Wherein（n1x, n1y, n1z）It is coordinate of the n1 points in CS6, the rest may be inferred for remaining.ri1、ri2、ri3、ri5、ri6
Can be by formula（2）~（6）Calculate.
（2）
（3）
（4）
(5)
(6)
Formula（2）~（6）In αi1、αi2、αi3、αi4Can be by formula（7）It is calculated：
（7）
Formula（7）InP ij 、q ij Withk ij Can be by equation group（8）It is calculated：
（8）
7th step of the inventive method, it is the demarcation for realizing magnetic field sources initial attitude.Rotation between CSr to CSs is closed
System is expressed as Rrs, r=1-7, s=1-7（Represent seven coordinate systems defined in table 1）.In the coordinate system that table 1 defines, CS1 is magnetic
The original coordinate system of field source 1, and system coordinate system.CS2 is 2 preferable original coordinate system of magnetic field sources, its y, z-axis and CS1
Y, z-axis is parallel, and x-axis overlaps with CS1 x-axis, i.e. CS2 coordinate origin is former with CS1 coordinate system in CS1 x-axis, but not
Point overlaps；But in actual placement magnetic field sources, the relation between two magnetic field sources may can not reach above-mentioned ideal situation, because
This defines the actual original coordinate system CS7 of magnetic field sources 2 again, then the demarcation to magnetic field sources initial attitude changes into searching magnetic field sources
Rotation relationship between 2 preferable original coordinate system CS2 and its current coordinate system CS4, that is, obtain R24。
CS1 to CS3 spin matrix can utilize what measurement obtainedφ 11 Withθ 11 By formula（9）It is calculated：
(9)
Equally can be by formula（10）Calculate CS7 to CS4 spin matrix：
(0)
Assuming that CS6 origin is moved to CS1 origin, and make CS6 x-axis orientation sensor, can be by formula（11）Try to achieve
CS6 to CS3 spin matrixs：
(11)
In formula (11),ω 0 ', θ 0' andφ 0' for assume CS6 x-axis orientation sensor when required rotation Eulerian angles.For
Solution ω0 ’, movable sensor, another mapping point is obtained, so that simultaneous is into equation.Keep CS6 and CS1 coordinate former
Point overlaps, and CS6 x-axis is pointed to the sensor after movement, can be by formula（12）Try to achieve CS6 to CS3 spin matrixs：
(12)
Due to CS1 and CS6 spin matrix be it is constant, i.e.,：
(13)
By formula（11) (13) are substituted into and can be obtained with (12)：
(14)
Equation group (14) is solved, can be obtainedWith, R can be obtained by substituting into formula (13)61。
Similarly, it is assumed that CS6 origin is moved to CS7 origin, and makes CS6 x-axis orientation sensor, can be by formula（15）
CS6 to CS4 spin matrix is obtained, whereinω 6 ', θ 6' andφ 6' it is required rotation when assuming CS6 x-axis orientation sensor
Eulerian angles：
(15)
(16)
Further according to formula（17）With（18）Formula can be obtained（19）：
(17)
(18)
(19)
Can be with push type by formula (10) and formula (19)（20）：
()
The rotation relationship between CS2 and CS4 has now been obtained, has passed through breakdown（20）In R24, that is, pass through formula（21）
The anglec of rotation after being corrected, ,：
()。
The magnetic tracking algorithm based on rotating excitation field is corrected according to calibration result, so as to improve positioning precision.
The present invention realizes demarcation by three axle micromotion platforms, while using the positioning function of electromagnetic tracking system in itself, can
Do not limited by spotting locus, significantly improve electromagnetic tracking system positioning precision.
Brief description of the drawings
Fig. 1 is that the system of the embodiment of the present invention forms.
Fig. 2 is the details block diagram of the device in Fig. 1.
Fig. 3 is the working-flow block diagram of embodiments of the invention.
Fig. 4 is the calibration principle of the present invention.
Embodiment
The present embodiment is with including two magnetic field sources（Magnetic field sources 1 and magnetic field sources 2）, the situation of more magnetic field sources can analogize
Arrive）, and illustrated exemplified by the electromagnetic tracking system that is encouraged using DC pulse mode of magnetic field sources.Fig. 1 is shown according to the present invention
The magnetic field sources relative tertiary location based on three axle micromotion platforms of design and the calibration system of initial attitude, including five parts：
Magnetic field sources 1, magnetic field sources 2, triaxial magnetic field sensor device 3, the axle micromotion platform 5 of control process display device 4 and three.Sensor
Device 3 is fixed on three axle micromotion platforms 5, and its accurate movement is controlled by micromotion platform 5.The space bit of magnetic field sources 1, magnetic field sources 2
Fixation is put, the distance between both origins are d, and initial attitude ideally is：The origin of magnetic field sources 2 is in magnetic field sources 1
X-axis on, each reference axis of two magnetic field sources is parallel to each other.Control process display device 4 exports DC pulse current, excitation field
Source 1, three axial coils of magnetic field sources 2, the bar magnet that simulation space is arbitrarily pointed to, magnetic field sources 1, magnetic field sources are output to by changing simultaneously
DC-pulse intensity of flow on 2 three axles, realizes the rotation of bar magnet.
The exploded block diagram of system components is as shown in Figure 2.Sensor device 3 selects three axle magnetoresistive transducers, including three axles
Component sensor 6,7 and 8, it is respectively intended to detect three orthogonal direction X ', Y ' and Z ' magnetic induction intensity.Sensor is exported after
Continuous signal condition and analog to digital（AD）Modular converter 9 is sent into control process display device 4.
Magnetic field sources 1,2 form by orthogonal three axis coil apparatus, are illustrated below by taking magnetic field sources 1 as an example（Magnetic field sources 2
Situation is similar, repeats no more）.Magnetic field sources 1 are made up of three groups of electromagnet coils 10,11 and 12, and coil is respectively by circuit 13,14 and
15 control drivings.It is required that three groups of coil geometric centers overlap, and to make the magnetic induction intensity that three axial coils synthesize in same distance
It is maximum at situation lower axis, and at this magnetic direction along axis.In the present embodiment, it is 2.5cm that three axial coils, which are wound on the length of side,
Cube on, the number of turn of each coil is 1000 circles.In addition, the pulse that electromagnet is exported by control process display device 4 is straight
Stream excitation.
Control process display device 4 is made up of control unit 18, algorithm unit 19, display output unit 20.Wherein：
Control unit 18 includes three parts：Sampling processing module 16, exciting current intensity control module 17 and fine motion are put down
Platform control module 29；Wherein：
Exciting current intensity control module 17 is controlled using DC pulse, is that control drive circuit 13,14,15 is realized to structure
Into the excitation of three axle quadrature coils 10,11 and 12 of magnetic field sources 1, in the present embodiment, bar magnet excitation uses pulse direct current mode,
Three periods of each cycle point, first period encourage three axle quadrature coils 10,11 and 12 synthesis simulation bar magnet 1；Second
Period excitation forms three quadrature coils of magnetic field sources 2（It is not drawn into）Synthesis simulation bar magnet 2；3rd period does not encourage,
Using the magnetic induction intensity that the magnetic induction intensity that measures of Magnetic Sensor and the 3rd period measure when simulating bar magnet excitation subtract each other as
Bar magnet is simulated in magnetic induction intensity caused by sensing station.The energisation mode of this pulse direct current is advantageous to eliminate environment metal
Interference is vortexed caused by material, and offsets earth's magnetic field and environment ferromagnetic material reasons for its use magnetic interference.For magnetic field sources 1
For（The situation of magnetic field sources 2 is identical, repeats no more）In first period of pulse direct current Energizing cycle, in x-axis emission lines
It is A to give amplitude on circle 10sin(φ)The exciting current of ampere, amplitude of being given on y-axis transmitting coil 11 is Acos(φ)Peace
The exciting current of training, 0 ampere of exciting current is given on z-axis transmitting coil 12, to synthesize size as A amperes, in x-y plane
RotationφThe bar magnet of degree, controlφChange in 0-2 π, when simulating bar magnet orientation sensor in x-y plane projecting direction, sensing
Device can detect maximum magnetic induction, record the anglec of rotation nowφ 1j .Afterwards, giving amplitude on x-axis transmitting coil 10 is
Asin(φ 1j )* sin(θ)The exciting current of ampere, it is A to give amplitude on y-axis transmitting coil 11cos(φ 1j ) * sin(θ)
The exciting current of ampere（φ 1j Simulate the anglec of rotation of the bar magnet in x-y plane orientation sensor）, while in z-axis emission lines
It is A to give amplitude on circle 12cos (θ)The exciting current of ampere, you can synthesis is in the simulation magnetic rotated perpendicular to x-y plane
Rod；ControlθIn 0- π（0-π/2）In the range of change, when simulating bar magnet orientation sensor, sensor can detect maximum magnetic strength
Intensity is answered, vertical rotary angle now is designated asθ 1j .In the above-mentioned methods, change is passed throughφ、θSimulation bar magnet can be achieved in space
Any sensing, and it is eventually pointed to Magnetic Sensor；
Micromotion platform control module 29, it is the movement for controlling micromotion platform X-axis 23, Y-axis 24 and Z axis 15, and thus drives
The Magnetic Sensor 26 being fixed on micromotion platform 5 is moved to selected n1, n2, n3（Overlapped with m1）, on five points of m2, m3；
Sampling processing module 16 be collection from detected by 26 3 axles of Magnetic Sensor 6,7,8, through signal condition and
The magnetic induction intensity signal that AD conversion 9 has digitized, and these signals are synthesized one had by way of vector summation
The magnetic flux density vector of size and Orientation.
Magnetic field sources 1 that algorithm unit 19 recorded according to above-mentioned steps, magnetic field sources 2 are pointed to from initial position rotary search and passed
The anglec of rotation of sensorφ ij 、θ ij ,By the formula in the content of the invention（1）-（8）, the origin for calculating magnetic field sources 1 and magnetic field sources 2 exists
Coordinate in CS6 coordinate systems, realize the demarcation to magnetic field sources origin；Formula in the content of the invention（9）- (21) obtain magnetic field sources
Rotation relationship between 1 and the initial position co-ordinates of magnetic field sources 2, realizes the demarcation to magnetic field sources initial attitude.
The calibration result that algorithm unit 19 obtains then is exported and shown by display output unit 20.
Fig. 3 is working-flow block diagram, illustrates to realize the links and order of demarcation, by step 30-36, most
The demarcation to magnetic field sources origin and initial attitude is realized eventually.
Fig. 4 show the schematic diagram for realizing magnetic field sources origin position calibration algorithm 32.The present invention is with the origin to magnetic field sources 1
Illustrate exemplified by demarcation, can be to more magnetic field sources with same procedure（Including magnetic field sources 2）Origin demarcated.The original of magnetic field sources 1
Point is positioned at the common center for three quadrature coils for forming magnetic field sources 1, i.e., the O1 points shown in Fig. 4.According in measurement process 37
It recordedφ ij 、θ ij , according to formula（1）-（8）Coordinate of the magnetic field sources 1 in CS6 coordinate systems can be tried to achieve（x1,y1,z1）；Together
Reason can try to achieve coordinate of the magnetic field sources 2 in CS6 coordinate systems（x2,y2,z2）.
The purpose of magnetic field sources initial attitude calibration algorithm module 36, it is in the case where system includes multiple magnetic field sources, obtains
Obtain the rotation relationship between each magnetic field sources initial attitude.In the present embodiment, it is the initial appearance of acquisition magnetic field sources 1 and magnetic field sources 2
Rotation relationship between state.Therefore, defining 7 coordinate systems shown in table 1, the problem of calibrating of initial attitude is converted into solution
Rotation relationship between coordinate system.The present invention is according to formula（9）-（21）Rotary course, finally give the rotation between CS4 to CS2
Transfer the registration of Party membership, etc. from one unit to another R24。
So far, that is, the electromagnetic tracking system magnetic field sources origin and initial attitude to being made up of multiple magnetic field sources are completed
Demarcation.Calibration result can be used for the location algorithm of amendment electromagnetic tracking system, significantly improve the positioning precision of system.
Claims (2)
1. a kind of magnetic field sources calibration system of the electromagnetic tracking system based on micromotion platform and rotating excitation field, it is characterised in that by following
Four parts form：Magnetic field sources, magnetic sensor device, control process display device and three axle micromotion platforms；Wherein：
The magnetic field sources have 2, are formed by orthogonal three axial coil and corresponding three control drive circuits；Orthogonal three axial coil
Three electromagnet coil geometric centers overlap；The origin of second magnetic field sources is in the X-axis of the first magnetic field sources, two magnetic field sources origins
The distance between be d, the Y-axis and Z axis of two magnetic field sources are parallel to each other；The electromagnet for forming magnetic field sources uses constant current exciting mode,
Every group of exciting current intensity is controlled by control process display device；Orthogonal three axial coil is simulating the magnetic that space is arbitrarily pointed to
Rod；
The magnet sensor arrangement is fixed on three axle micromotion platforms, and it is controlled in space accurate movement, survey by three axle micromotion platforms
Measure the magnetic induction intensity of three orthogonal directions；The triaxial magnetic field sensor device includes：Three axis component sensors, a signal
Conditioning and analog-digital conversion module, three axis component sensors are respectively intended to detect three orthogonal direction X ', Y ' and Z ' magnetic strength
Intensity is answered, it is exported is sent into control process display device through follow-up signal condition and analog-digital conversion module, by control
Manage the sampling processing module samples processing in display device；
The control process display device is controlled single by control unit, algorithm unit, display output unit and three axle micromotion platforms
Member composition, described control unit include three parts：Sampling processing module, exciting current intensity control module and micromotion platform control
Molding block, sampling processing module are the I/O mouths that microprocessor carries, and signal condition and analog to digital are come from for sampling processing
The signal of modular converter；Exciting current intensity control module is that microprocessor is right according to the simulation bar magnet anglec of rotation institute calculated
The exciting current for three quadrature coils of magnetic field sources answered, the control drive circuit of magnetic field sources is controlled by I/O mouths, there is provided to three axles
The excitation control of quadrature coil, synthesizes the required simulation bar magnet pointed to；Micromotion platform control module is that microprocessor passes through I/O mouths
Output signal, the movement of three axles of micromotion platform is controlled as requested, and thus drive three axle magnetic being fixed on micromotion platform
Sensor device is moved in selected coordinate points；
The algorithm unit according to simulation magnetic bar rotation searching and eventually points to obtain in sensor process in microprocessor internal
Rotation angle information, with origin calibration algorithm, calculate the first magnetic field sources, the origin of the second magnetic field sources；With initial
Posture calibration algorithm, the first calculating magnetic field source, the second magnetic field sources each reference axis initial sensing；
The display output unit is the liquid crystal display and I/O mouths being connected with microprocessor, for will be calculated by algorithm unit
Obtained calibration result is exported and shown over the display；
The three axles micromotion platform control unit is in microprocessor internal, and the instruction exported as requested by I/O mouths is to fine motion
Three the mobile of axle of platform are accurately controlled；
The three axles micromotion platform by three mutually orthogonal tracks and can the fixing device of accurate movement in orbit form, use
In control magnetic sensor in space accurate movement.
2. a kind of magnetic field sources calibration system based on described in claim 1, it is characterised in that determined first according to right-hand rule
Adopted seven coordinate systems as shown in table 1, wherein CS1 is global coordinate system, and CS6 is micromotion platform coordinate system, and during calibration
Reference coordinate system；
The coordinate system of table 1 defines
Comprise the following steps that：
Step 1: calibration system is initialized；
Step 2: space known coordinate point is shifted to by three axle micromotion platforms control magnetic sensor device；
Step 3: the simulation bar magnet corresponding to the first magnetic field sources and the second magnetic field sources, searches for and points to the three axles magnetic sensing
Device device；
Step 4: the bar magnet that the first magnetic field sources of record, the second magnetic field sources are simulated is from initial position to sensing magnetic sensor
The horizontal and vertical anglec of rotation during device；
Step 5: judging whether three axle micromotion platforms have moved to the selected known coordinate in five, space by magnetic sensor device
Point, if NO, then repeat step three, step 4；If YES, then six are gone to step；
Step 6: with magnetic field sources origin calibration algorithm, the first magnetic field sources, the origin of the second magnetic field sources are calculated；
Step 7: with magnetic field sources initial attitude calibration algorithm, calculate the first magnetic field sources, each reference axis of the second magnetic field sources just
Begin to point to；
Calibration system described in step 1 is initialized, and after referring to start, three axle micromotion platforms, the are controlled by control process display device
One magnetic field sources and the second magnetic field sources move/turned to respective initial position；
Space known coordinate point is shifted to by three axle micromotion platforms control magnetic sensor device described in step 2, is by three axles
Micromotion platform control unit controls three axle movements of micromotion platform respectively, and magnetic sensor device is placed in selected known seat
Punctuate；If selected known coordinate point is 5：N1, n2, n3, m2, m3, if m1 overlaps with n3, these coordinate points meet following bar
Part：
Point-blank, and the spacing between n1, n2 is equal with the spacing between n2, n3 by n1, n2, n3；M1, m2, m3 be not
With on the another straight line of n1, n2, n3 straight line parallel formed, and the spacing between m1, m2 and the spacing phase between m2, m3
Deng；
Described in step 3 with the first magnetic field sources and the second magnetic field sources corresponding to simulation bar magnet, search for and point to the three axles magnetic and pass
Sensor arrangement, the first magnetic field sources and second being made up of exciting current intensity control module alternative excitation orthogonal three axial coil
Magnetic field sources, simulate two rotatable bar magnets；Specifically energisation mode is：If form three quadrature coils of magnetic field sources crosses the center of circle
Axle is respectively x-axis, y-axis, z-axis, and in first period of Energizing cycle, on x-axis transmitting coil giving amplitude is
The exciting current of ampere, on y-axis transmitting coil giving amplitude isThe exciting current of ampere, pacified using synthesizing size as A
Training, rotated in x-y planeThe bar magnet of degree, controlChange in 0-2 π, when simulation bar magnet orientation sensor projects in x-y plane
During direction, sensor can detect the maximum magnetic induction in x-y plane；Afterwards, giving amplitude on x-axis transmitting coil isThe exciting current of ampere, giving amplitude on y-axis transmitting coil isThe excitation electricity of ampere
Stream,Simulate the anglec of rotation of the bar magnet when x-y plane orientation sensor projects；Now width is given on z-axis transmitting coil
Spend for AThe exciting current of ampere, that is, synthesize in the simulation bar magnet rotated perpendicular to x-y plane；ControlIn 0- π scopes
Interior change, when simulating bar magnet orientation sensor, sensor detects maximum magnetic induction, and note now simulates bar magnet vertical
The anglec of rotation of plane is
The first magnetic field sources are recorded described in step 4, the bar magnet that the second magnetic field sources are simulated senses from initial position to three axle magnetic are pointed to
The horizontal and vertical anglec of rotation during device device, i.e. horizontal rotation angleAnd vertical rotation angleWherein i=1-2 pairs
Point known to the coordinate of five, space should be corresponded in two magnetic field sources, j=1-5, similarly hereinafter；
Magnetic field sources origin calibration algorithm, recorded according to step 4 described in step 6WithCalculate the first magnetic field
Origin (x1, y1, z1), (x2, y2, the z2) of source, the second magnetic field sources in micromotion platform coordinate system, its formula are：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>n</mi>
<mn>1</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>n</mi>
<mn>1</mn>
<mi>y</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>n</mi>
<mn>1</mn>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>=</mo>
<msubsup>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>n</mi>
<mn>2</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
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<mrow>
<msub>
<mi>y</mi>
<mi>i</mi>
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<mo>-</mo>
<mi>n</mi>
<mn>2</mn>
<mi>y</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>n</mi>
<mn>2</mn>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>=</mo>
<msubsup>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mrow>
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<mrow>
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<mi>x</mi>
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<mi>n</mi>
<mn>3</mn>
<mi>x</mi>
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<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
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<mrow>
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<mi>y</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>n</mi>
<mn>3</mn>
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</mrow>
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</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
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<mrow>
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<mi>z</mi>
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</msub>
<mo>-</mo>
<mi>n</mi>
<mn>3</mn>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>=</mo>
<msubsup>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
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<mo>-</mo>
<mi>m</mi>
<mn>2</mn>
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</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>m</mi>
<mn>2</mn>
<mi>y</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>m</mi>
<mn>2</mn>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>=</mo>
<msubsup>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mn>5</mn>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>m</mi>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>m</mi>
<mn>3</mn>
<mi>y</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>m</mi>
<mn>3</mn>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>=</mo>
<msubsup>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mn>6</mn>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein (n1x, n1y, n1z) is coordinate of the n1 points in CS6, and the rest may be inferred for remaining, (xi,yi,zi) sat for magnetic field sources origin
Mark；ri1、ri2、ri3、ri5、ri6Then calculated by set below formula：
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>d</mi>
<mi> </mi>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msqrt>
<mrow>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>2</mn>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msqrt>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi> </mi>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msqrt>
<mrow>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>2</mn>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msqrt>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>d</mi>
<mi> </mi>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msqrt>
<mrow>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>2</mn>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msqrt>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mn>5</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi> </mi>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msqrt>
<mrow>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>2</mn>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
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</mrow>
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<mrow>
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<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msqrt>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mn>6</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>d</mi>
<mi> </mi>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msqrt>
<mrow>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>2</mn>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msqrt>
</mfrac>
</mrow>
α thereinijThen obtained by following formula：
<mrow>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mn>2</mn>
</mfrac>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>q</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>q</mi>
<mrow>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>k</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>k</mi>
<mrow>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mrow>
3
I=1,2, j=1,2,3,4；
Magnetic field sources initial attitude calibration algorithm described in step 7, according to table 1, the rotation relationship between CSr to CSs is expressed as
Rrs, r=1-7, s=1-7, the demarcation to magnetic field sources initial attitude, which changes into, finds the second magnetic field sources ideal original coordinate system CS2
Rotation relationship between its current coordinate system CS4, that is, obtain R24：
θ′7, ω '7For the anglec of rotation after being corrected.
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